This invention generally relates to the manufacture of paper and paperboard products. In particular, the invention relates to engineering and manufacture of grades of paper and paperboard products having improved web runnability.
Fracture toughness is an inherent (mechanical) property of every material. In essence, it is the ability of the material to carry loads or deform plastically in the presence of a notch or a defect. In other words, fracture toughness measures the material""s ability to resist propagation of a pre-existing crack. In this respect, fracture-toughness testing of paper or paperboard, a complex network of essentially cellulosic fibers, should be constituted within the rubric of established methodologies in fracture mechanics and materials science. More crucially, fracture toughness has been found to be a good predictor of pressroom runnability [Page, D. H., and Seth, R. S., xe2x80x9cThe problem of pressroom runnability,xe2x80x9d TAPPI J., 65(8), 92 (1982)], and, in general, end-use performance of paper and paperboard products [Seth, R. S., and Page, D. H., xe2x80x9cFracture resistance: a failure criterion for paper,xe2x80x9d TAPPI J., 58(9), 112 (1975)].
Crack propagation in cellulosic networks would essentially arise from the development of near- or above-threshold stresses as a result of (external) mechanical, thermal and/or hygroscopic loading, or due to the presence of defects (in whatever form or shape: e.g., defects, shives, irregular web edges, etc.). It should thus become customary within the papermaking industry that fracture toughness be reported alongside elastic moduli and tensile strengths, since it is a fundamental mechanical property that is intrinsically linked to the overall (mechanical) performance of paper or paperboard products. Moreover, fracture toughness can function as an accurate predictor of the performance of paper during manufacturing, printing or converting operations. In all of these operations and most end-use scenarios, external loading is applied in the plane of the paper sheet/web; and if the latter develops high stresses that lead to the propagation of cracks and ultimately failure, that will unequivocally occur in the plane of the paper sheet or web, too. It thus seems sound, particularly from a mechanics-of-materials viewpoint, that assessment of web runnability in presses, converting and end-use performance be principally addressed in terms of the paper fracture toughness. A corollary to the aforesaid would be: engineering better (mechanical) performance during printing and converting, product integrity, reliability and durability for (general) end-use needs to be attempted by primarily, but not exclusively, addressing the material""s fracture toughness. In this light, customary industry practice of using out-of-plane tear, via the Elmendorf or Brecht-Imset tests, as a predictor of operational and end-use mechanical performance should be abandoned since it characterizes fracture phenomena occurring in the wrong plane, and thus produces irrelevant results. Moreover, neither the Elmendorf nor the Brecht-Imset tear test characterizes deformation beyond the elastic scope.
Three primary factors control the susceptibility of a material to fracture: fracture toughness, crack size and stress level. These primary factors are in turn influenced by other considerations. In the case of paper, they are influenced by papermaking variables (e.g., % filler, refining consistency, Kraft to groundwood ratio), environment (temperature and moisture), stress concentration (presence and size of defects), residual stresses, etc. Instituting an appropriate test for the material""s fracture toughness would be the first step to understanding its resistance to cracking, or lack thereof. An appropriate test would essentially depend on the failure mode and the nature of the fracture region (elastic, elastic-plastic or fully plastic). Two considerations are relevant for paper and paper products"" end-use performance: a) All failures in print presses and converting operations occur in the plane of the paper sheet or web; b) Owing to the highly viscoelastic nature of the cellulosic network, the zone ahead of the propagating crack tip is appreciably plastic. Based on these considerations, a test is required whereby a notched specimen is loaded in tension in the plane of the specimen. The rate of applying tensile loading must be such that stable crack propagation is ensured.
Paper is a tough elastic-plastic material with a low yield stress. When strained, paper yields not only at the crack tip where the strains are high, but also the material away from the crack tip can yield (refer to FIG. 1). This, which results because the material resists crack propagation and requires larger strains for the crack to propagate, substantially complicates fracture toughness testing. It is thus indicated that permanent deformation is no longer confined to the fracture process zone (the zone ahead of the crack tip where fiber breakage and bond breakage are concentrated) as it is for an elastic material, but can spread throughout the material. The extent of deformation away from the crack depends on the size of the crack relative to the specimen width and on the toughness of the material. Thus, in addition to work consumed in the fracture process zone (work essential to fracture), work is also consumed in the yielded regions away from the crack tip (work not essential to fracture). The area under the load versus elongation curve (see FIG. 2) of the fractured material represents the total work of fracture, i.e., the combination of contributions to fracture and remote deformation. Separating these two contributions (a non-trivial task) makes possible the estimation of fracture toughness, or the essential work of fracture: work done per unit new crack area [see Cotterell, B., and Reddel, J. K., xe2x80x9cThe essential work of plane stress ductile fracture,xe2x80x9d Int. J. Fracture 13(3), 267 (1977)].
Two approaches have mainly been followed for measuring the in-plane fracture toughness of tough ductile paper: the xe2x80x9cJ-integralxe2x80x9d approach and the xe2x80x9cessential work of fracturexe2x80x9d approach. One important consideration in choosing an approach should be the ability to determine the material property independent of specimen size. (Large changes can occur in the load versus elongation behavior of paper when, for example, refining energies are increased/decreased, and it thus becomes imperative that the instituted test measure the real fracture toughness of the sample and not some artifacts of the test.) Two significant issues are associated with conducting J-integral testing: a) Several research findings published in the open literature indicate that fracture toughness results independent of specimen size and crack geometry were not obtained; b) A crucial consideration in the J-integral calculations would be to precisely identify the onset of crack initiation in a specimen. This is an extremely complex point and may only precisely be addressed by utilizing what is referred to as the direct-current potential difference method, which has successfully been used, for instance, for J-integral determination of fracture toughness for steel. This approach, which basically correlates crack propagation with the electrical potential difference and hence identifies very precisely the onset of crack initiation, is excruciatingly laborious to execute. It has, perhaps, therefore not been adopted for paper testing in any research laboratory within industrial or academic centers. On the other hand, the essential work of fracture (e.w.f.) method was shown to give results independent of specimen size [see Seth, R. S., Robertson, A. G., Mai, Y-W. and Hoffmann, J. D., xe2x80x9cPlane stress fracture toughness of paper,xe2x80x9d TAPPI J. 76(2), 109 (1993) and Seth, R. S., xe2x80x9cPlane stress fracture toughness and its measurement for paper,xe2x80x9d in: Products of Papermaking, Trans. of Tenth Fund. Res. Symp., Oxford, C. F. Baker (ed.), PIRA International, Leatherhead, Surrey, U. K., p. 1529 (1993)] and, more critically, because of the set-up involved, no onset of crack initiation is required for determining the final calculations. Within the constraints of available tools in fracture mechanics, the e.w.f. method is the easiest and best assessor of fracture toughness of paper and paperboard.
There is a need to develop a fundamental understanding of what and how papermaking variables affect the fracture toughness of paper and paperboard. Such an understanding would enable the better design of products, such as lightweight coated grades of paper, for optimal runnability.
The present invention is a method of manufacturing paper or paperboard using a design approach based on fracture toughness for achieving improved runnability, e.g., minimal web breaks in presses. The fracture toughness-based approach disclosed herein can be utilized to cost-effectively design grades of paper, e.g., through minimizing raw material intake. Although the examples disclosed below pertain to lightweight coated grades of paper, the fracture toughness-based approach of the present invention is more encompassing and can be applied to the design of all paper and paperboard grades. The fracture toughness-based approach also makes possible the optimization of pulping and papermaking variables, such as fiber length, viscosity, etc.
In accordance with the preferred embodiment of the invention, a mathematical model is used to design paper and paperboard having improved runnability. The mathematical model provides an estimate of fracture toughness for an optimized paper product based on specific measurement parameters, e.g., filler percent, softwood content and caliper for optimal fracture toughness. After the optimizing set of measurement parameters has been acquired, these parameters can be used to manufacture grades of paper having improved runnability performance, e.g., in printing presses.
To arrive at a mathematical model, a factorial experiment was carried out to investigate the effects of papermaking variables on the in-plane fracture toughness, an inherent mechanical property of paper. A statistically significant model for fracture toughness as a function of filler percent, softwood content and caliper resulted from the rigorous experimental testing and analysis. The experimental results showed that fracture toughness decreases with increasing filler content; and, for a specific filler content, fracture toughness increases by about 10% when the softwood content is increased by around 4%. If the caliper is doubled, keeping the softwood and filler contents the same, fracture toughness increases by about 50%. Modeling of fracture toughness holds meaningful results for the machine direction (MD) only. Concomitantly, stiffness was found to be proportional to basis weight and caliper and inversely proportional to filler content.
Furthermore, it was found that fracture toughness does not correlate, in either the cross direction (CD) or the machine direction, with the elasticity modulus, tensile strength, stiffness, tear or formation index, when considered for a specific caliper range. The experimental findings revealed the important role fracture toughness plays in affecting a sheet""s performance. Fracture toughness is an important design consideration for optimal web runnability and general end use performance of, for example, lightweight coated (LWC) grades. In accordance with the preferred embodiment of the invention, the mathematical model provides a basis for outlining critical operating parameters for optimal fracture toughness performance within a papermaking mill.